Every temperature measuring process involves the transfer of heat from the measured body to the measuring device probe. Heat may be transferred in three ways; by conduction, by convection and by radiation. The method of the present invention measures heat convection as well as heat conduction (such as in streaming air or liquids). Radiation heat meant lacks accuracy since achieving accuracy is dependent on earlier knowledge of constants that are not known with a high certainty.
Most temperature measuring devices using convection or conduction require the temperature measuring sensor to come into thermal equilibrium with the body being measure. When the body being measured is a poor heat conductor, the time to reach equilibrium (with the temperature measuring sensor) may be considerable. This measurement waiting time (to reach equilibrium) is a thermodynamic necessity. Various methods aiming at shortening this waiting time exist. For example DE 3527942 and U.S. Pat. No. 4,183,248 disclose a method comprising two temperature sensors and a heating elements. Shortening of this wait time is always at the expense of the accuracy of measurement.
The device of the present invention eliminates this waiting time. Instead of directly measuring the temperature (which requires waiting for equilibrium), the device of the present invention calculates the temperature by predicting temperature sensor measurements. This prediction relies on a heat transfer equation, and preferably a heat conduction equation whereby the body temperature is calculated according to heat flux measured (a) between the body and a first temperature sensor and (b) between the first temperature sensor and a second temperature sensor (or sensors). Since firstly the heat flux measurements do not require waiting for thermal equilibrium and secondly the calculation per se is performed in real time on a standard micro-processor, the device of the present invention can rapidly display the accurate temperature of the body.
Following is a detailed explanation of deriving the essential equations (embodied within the algorithm used by the data processing limit according to the present invention).
The Conduction Heat Transfer Equation (one dimensional without heat sources, since the heating body of the present device is not operated during the temperature measurement): ##EQU1##
This equation represents heat flux differences between the inlet and the outlet of the body under discussion. ##EQU2##
where one dimensional heat flux (Q) is defined as the constant "k" times the change in temperature dT with regard to a change in position dx: ##EQU3##
Using finite differences equation (*) can be written: ##EQU4##
If: ##EQU5##
and ##EQU6##
Then: ##EQU7##
If there are two heat sensors "S.sub.1 " which is located at x.sub.in and "S.sub.2 " which is located at x.sub.out, and these sensors are separated by a finite distance having a known thermal conduction coefficient (e.g a thermal insulation member), and "S.sub.1 " is in thermal contact with the body, and "S.sub.2 " is within a thermal probe, and the body is located at x.sub.in +.DELTA.x then from (**) it is clearly seen that approximately: ##EQU8##
The temperature rise as evaluated at location 1/2(x.sub.in +x.sub.out) is defined as heat in from the body .omega..sub.in times: [(T.sub.body) minus (T.sub.s.sub..sub.1 )] minus .omega..sub.out times heat out from the probe [(T.sub.s.sub..sub.1 ) minus (T.sub.2.sub..sub.2 )}.
The device of the present invention solves this equation for the unknown T.sub.body, .omega..sub.in, .omega..sub.out according to measured temperatures representing the heat fluxes, without any need to wait for thermal equilibrium.